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A clothing store needs to order new inventory. It has three different types of hats for sale: straw hats, beanies, and cowboy hats. The straw hat is priced at $13.99, the beanie at $7.99, and the cowboy hat at $14.49. If 100 hats were sold this past quarter, $1,119 was taken in by sales, and the amount of beanies sold was 10 more than cowboy hats, how many of each should the clothing store order to replace those already sold

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Answer:

10 straw hats, 40 cowboy hats and 50 beanies.

Step-by-step explanation:

Let 'S' denote straw hats, 'B' denote beanies and 'C' denote cowboy hats.

The number of hats sold, total income and relationship between beanies and cowboy hats are:

[tex]S+B+C=100\\13.99S+7.99B+14.49C=1,119\\B=10+C[/tex]

Solving the linear system:

[tex]S+2C=90\\13.99S+7.99(10+C)+14.49C=1,119\\\\S+2C=90\\13.99S+22.48C=1,039.1\\\\(13.99-11.24)S=1,039.1-90*11.24\\2.75S=27.5\\S=10\\\\C=\frac{90-S}{2}\\ C=40\\\\B=10+C\\B=50[/tex]

The store should order 10 straw hats, 40 cowboy hats and 50 beanies.

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